LMFDB - Embedded newform 588.2.e.f.491.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(491,588)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("588.491");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.e (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			491.23
Character	$\chi$	$=$	588.491
Dual form			588.2.e.f.491.21

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.29871 + 0.559784i) q^{2} +(-1.60392 + 0.653796i) q^{3} +(1.37328 + 1.45399i) q^{4} +3.97283i q^{5} +(-2.44900 - 0.0487576i) q^{6} +(0.969574 + 2.65705i) q^{8} +(2.14510 - 2.09727i) q^{9} +(-2.22392 + 5.15954i) q^{10} -3.30344 q^{11} +(-3.15325 - 1.43424i) q^{12} +0.850601 q^{13} +(-2.59742 - 6.37208i) q^{15} +(-0.228181 + 3.99349i) q^{16} -0.576468i q^{17} +(3.95988 - 1.52295i) q^{18} -3.59139i q^{19} +(-5.77645 + 5.45582i) q^{20} +(-4.29021 - 1.84921i) q^{22} +3.96171 q^{23} +(-3.29229 - 3.62779i) q^{24} -10.7833 q^{25} +(1.10468 + 0.476153i) q^{26} +(-2.06938 + 4.76630i) q^{27} +3.37929i q^{29} +(0.193706 - 9.72947i) q^{30} -4.89898i q^{31} +(-2.53183 + 5.05864i) q^{32} +(5.29845 - 2.15978i) q^{33} +(0.322697 - 0.748663i) q^{34} +(5.99525 + 0.238815i) q^{36} +4.29021 q^{37} +(2.01040 - 4.66416i) q^{38} +(-1.36429 + 0.556119i) q^{39} +(-10.5560 + 3.85195i) q^{40} +5.35550i q^{41} +7.66518i q^{43} +(-4.53656 - 4.80318i) q^{44} +(8.33208 + 8.52212i) q^{45} +(5.14510 + 2.21770i) q^{46} -9.09050 q^{47} +(-2.24494 - 6.55441i) q^{48} +(-14.0044 - 6.03634i) q^{50} +(0.376892 + 0.924607i) q^{51} +(1.16812 + 1.23677i) q^{52} -0.608639i q^{53} +(-5.35562 + 5.03163i) q^{54} -13.1240i q^{55} +(2.34803 + 5.76029i) q^{57} +(-1.89167 + 4.38871i) q^{58} +7.87961 q^{59} +(5.69797 - 12.5273i) q^{60} +9.74629 q^{61} +(2.74237 - 6.36234i) q^{62} +(-6.11985 + 5.15242i) q^{64} +3.37929i q^{65} +(8.09014 + 0.161068i) q^{66} +9.04574i q^{67} +(0.838179 - 0.791654i) q^{68} +(-6.35425 + 2.59015i) q^{69} +9.15654 q^{71} +(7.65239 + 3.66619i) q^{72} +1.41421 q^{73} +(5.57172 + 2.40159i) q^{74} +(17.2956 - 7.05010i) q^{75} +(5.22185 - 4.93200i) q^{76} +(-2.08312 - 0.0414733i) q^{78} -6.92820i q^{79} +(-15.8654 - 0.906525i) q^{80} +(0.202931 - 8.99771i) q^{81} +(-2.99792 + 6.95523i) q^{82} +4.13877 q^{83} +2.29021 q^{85} +(-4.29084 + 9.95483i) q^{86} +(-2.20936 - 5.42010i) q^{87} +(-3.20293 - 8.77742i) q^{88} +5.75676i q^{89} +(6.05039 + 15.7319i) q^{90} +(5.44055 + 5.76029i) q^{92} +(3.20293 + 7.85756i) q^{93} +(-11.8059 - 5.08871i) q^{94} +14.2680 q^{95} +(0.753530 - 9.76894i) q^{96} +13.5487 q^{97} +(-7.08622 + 6.92820i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{16} - 12 q^{18} - 24 q^{25} - 48 q^{30} + 12 q^{36} + 72 q^{46} - 24 q^{57} + 72 q^{58} + 72 q^{60} - 48 q^{64} + 108 q^{72} - 24 q^{78} - 24 q^{81} - 48 q^{85} - 48 q^{88} + 48 q^{93}+O(q^{100}) $ 24 * q - 24 * q^16 - 12 * q^18 - 24 * q^25 - 48 * q^30 + 12 * q^36 + 72 * q^46 - 24 * q^57 + 72 * q^58 + 72 * q^60 - 48 * q^64 + 108 * q^72 - 24 * q^78 - 24 * q^81 - 48 * q^85 - 48 * q^88 + 48 * q^93

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.29871	+	0.559784i	0.918325	+	0.395827i
$2$	1.29871	+	0.559784i	0.918325	+	0.395827i
$3$	−1.60392	+	0.653796i	−0.926022	+	0.377469i
$3$	−1.60392	+	0.653796i	−0.926022	+	0.377469i
$4$	1.37328	+	1.45399i	0.686642	+	0.726996i
$5$			3.97283i			1.77670i	0.459165	+	0.888351i	$0.348149\pi$
$5$			3.97283i			1.77670i	−0.459165	+	0.888351i	$0.651851\pi$
$6$	−2.44900	−	0.0487576i	−0.999802	−	0.0199052i
$7$		0			0
$7$		0			0
$8$	0.969574	+	2.65705i	0.342796	+	0.939410i
$9$	2.14510	−	2.09727i	0.715034	−	0.699089i
$10$	−2.22392	+	5.15954i	−0.703266	+	1.63159i
$11$	−3.30344			−0.996025			−0.498013	−	0.867170i	$-0.665937\pi$
$11$	−3.30344			−0.996025			−0.498013	+	0.867170i	$0.665937\pi$
$12$	−3.15325	−	1.43424i	−0.910264	−	0.414028i
$13$	0.850601			0.235914			0.117957	−	0.993019i	$-0.462365\pi$
$13$	0.850601			0.235914			0.117957	+	0.993019i	$0.462365\pi$
$14$		0			0
$15$	−2.59742	−	6.37208i	−0.670650	−	1.64527i
$16$	−0.228181	+	3.99349i	−0.0570454	+	0.998372i
$17$		−	0.576468i		−	0.139814i	−0.997554	−	0.0699070i	$-0.977730\pi$
$17$		−	0.576468i		−	0.139814i	0.997554	−	0.0699070i	$-0.0222702\pi$
$18$	3.95988	−	1.52295i	0.933352	−	0.358962i
$19$		−	3.59139i		−	0.823921i	−0.911202	−	0.411960i	$-0.864844\pi$
$19$		−	3.59139i		−	0.823921i	0.911202	−	0.411960i	$-0.135156\pi$
$20$	−5.77645	+	5.45582i	−1.29165	+	1.21996i
$21$		0			0
$22$	−4.29021	−	1.84921i	−0.914675	−	0.394254i
$23$	3.96171			0.826073			0.413037	−	0.910714i	$-0.364468\pi$
$23$	3.96171			0.826073			0.413037	+	0.910714i	$0.364468\pi$
$24$	−3.29229	−	3.62779i	−0.672035	−	0.740519i
$25$	−10.7833			−2.15667
$26$	1.10468	+	0.476153i	0.216646	+	0.0933812i
$27$	−2.06938	+	4.76630i	−0.398253	+	0.917276i
$28$		0			0
$29$			3.37929i			0.627518i	0.949503	+	0.313759i	$0.101588\pi$
$29$			3.37929i			0.627518i	−0.949503	+	0.313759i	$0.898412\pi$
$30$	0.193706	−	9.72947i	0.0353656	−	1.77635i
$31$		−	4.89898i		−	0.879883i	−0.898027	−	0.439941i	$-0.854999\pi$
$31$		−	4.89898i		−	0.879883i	0.898027	−	0.439941i	$-0.145001\pi$
$32$	−2.53183	+	5.05864i	−0.447569	+	0.894250i
$33$	5.29845	−	2.15978i	0.922341	−	0.375969i
$34$	0.322697	−	0.748663i	0.0553421	−	0.128395i
$35$		0			0
$36$	5.99525	+	0.238815i	0.999208	+	0.0398026i
$37$	4.29021			0.705305			0.352653	−	0.935754i	$-0.385280\pi$
$37$	4.29021			0.705305			0.352653	+	0.935754i	$0.385280\pi$
$38$	2.01040	−	4.66416i	0.326130	−	0.756627i
$39$	−1.36429	+	0.556119i	−0.218462	+	0.0890503i
$40$	−10.5560	+	3.85195i	−1.66905	+	0.609047i
$41$			5.35550i			0.836389i	0.908357	+	0.418195i	$0.137337\pi$
$41$			5.35550i			0.836389i	−0.908357	+	0.418195i	$0.862663\pi$
$42$		0			0
$43$			7.66518i			1.16893i	0.811419	+	0.584464i	$0.198695\pi$
$43$			7.66518i			1.16893i	−0.811419	+	0.584464i	$0.801305\pi$
$44$	−4.53656	−	4.80318i	−0.683913	−	0.724106i
$45$	8.33208	+	8.52212i	1.24207	+	1.27040i
$46$	5.14510	+	2.21770i	0.758604	+	0.326982i
$47$	−9.09050			−1.32599			−0.662993	−	0.748626i	$-0.730714\pi$
$47$	−9.09050			−1.32599			−0.662993	+	0.748626i	$0.730714\pi$
$48$	−2.24494	−	6.55441i	−0.324029	−	0.946047i
$49$		0			0
$50$	−14.0044	−	6.03634i	−1.98052	−	0.853667i
$51$	0.376892	+	0.924607i	0.0527754	+	0.129471i
$52$	1.16812	+	1.23677i	0.161989	+	0.171509i
$53$		−	0.608639i		−	0.0836029i	−0.999126	−	0.0418015i	$-0.986690\pi$
$53$		−	0.608639i		−	0.0836029i	0.999126	−	0.0418015i	$-0.0133097\pi$
$54$	−5.35562	+	5.03163i	−0.728808	+	0.684718i
$55$		−	13.1240i		−	1.76964i
$56$		0			0
$57$	2.34803	+	5.76029i	0.311005	+	0.762969i
$58$	−1.89167	+	4.38871i	−0.248389	+	0.576266i
$59$	7.87961			1.02584			0.512919	−	0.858437i	$-0.328564\pi$
$59$	7.87961			1.02584			0.512919	+	0.858437i	$0.328564\pi$
$60$	5.69797	−	12.5273i	0.735604	−	1.61727i
$61$	9.74629			1.24789			0.623943	−	0.781470i	$-0.285530\pi$
$61$	9.74629			1.24789			0.623943	+	0.781470i	$0.285530\pi$
$62$	2.74237	−	6.36234i	0.348281	−	0.808018i
$63$		0			0
$64$	−6.11985	+	5.15242i	−0.764982	+	0.644052i
$65$			3.37929i			0.419149i
$66$	8.09014	+	0.161068i	0.995828	+	0.0198261i
$67$			9.04574i			1.10511i	0.833475	+	0.552557i	$0.186348\pi$
$67$			9.04574i			1.10511i	−0.833475	+	0.552557i	$0.813652\pi$
$68$	0.838179	−	0.791654i	0.101644	−	0.0960021i
$69$	−6.35425	+	2.59015i	−0.764962	+	0.311817i
$70$		0			0
$71$	9.15654			1.08668			0.543341	−	0.839512i	$-0.317159\pi$
$71$	9.15654			1.08668			0.543341	+	0.839512i	$0.317159\pi$
$72$	7.65239	+	3.66619i	0.901842	+	0.432065i
$73$	1.41421			0.165521			0.0827606	−	0.996569i	$-0.473626\pi$
$73$	1.41421			0.165521			0.0827606	+	0.996569i	$0.473626\pi$
$74$	5.57172	+	2.40159i	0.647700	+	0.279179i
$75$	17.2956	−	7.05010i	1.99712	−	0.814076i
$76$	5.22185	−	4.93200i	0.598987	−	0.565739i
$77$		0			0
$78$	−2.08312	−	0.0414733i	−0.235867	−	0.00469593i
$79$		−	6.92820i		−	0.779484i	−0.920924	−	0.389742i	$-0.872564\pi$
$79$		−	6.92820i		−	0.779484i	0.920924	−	0.389742i	$-0.127436\pi$
$80$	−15.8654	−	0.906525i	−1.77381	−	0.101353i
$81$	0.202931	−	8.99771i	0.0225479	−	0.999746i
$82$	−2.99792	+	6.95523i	−0.331065	+	0.768077i
$83$	4.13877			0.454289			0.227144	−	0.973861i	$-0.427061\pi$
$83$	4.13877			0.454289			0.227144	+	0.973861i	$0.427061\pi$
$84$		0			0
$85$	2.29021			0.248408
$86$	−4.29084	+	9.95483i	−0.462693	+	1.07346i
$87$	−2.20936	−	5.42010i	−0.236869	−	0.581096i
$88$	−3.20293	−	8.77742i	−0.341434	−	0.935676i
$89$			5.75676i			0.610216i	0.952318	+	0.305108i	$0.0986925\pi$
$89$			5.75676i			0.610216i	−0.952318	+	0.305108i	$0.901307\pi$
$90$	6.05039	+	15.7319i	0.637768	+	1.65829i
$91$		0			0
$92$	5.44055	+	5.76029i	0.567217	+	0.600552i
$93$	3.20293	+	7.85756i	0.332128	+	0.814791i
$94$	−11.8059	−	5.08871i	−1.21769	−	0.524861i
$95$	14.2680			1.46386
$96$	0.753530	−	9.76894i	0.0769069	−	0.997038i
$97$	13.5487			1.37567			0.687833	−	0.725869i	$-0.258562\pi$
$97$	13.5487			1.37567			0.687833	+	0.725869i	$0.258562\pi$
$98$		0			0
$99$	−7.08622	+	6.92820i	−0.712192	+	0.696311i
$100$	−14.8086	−	15.6789i	−1.48086	−	1.56789i
$101$		−	7.13944i		−	0.710401i	−0.934790	−	0.355200i	$-0.884413\pi$
$101$		−	7.13944i		−	0.710401i	0.934790	−	0.355200i	$-0.115587\pi$
$102$	−0.0281072	+	1.41177i	−0.00278303	+	0.139786i
$103$			10.5088i			1.03546i	0.855543	+	0.517732i	$0.173224\pi$
$103$			10.5088i			1.03546i	−0.855543	+	0.517732i	$0.826776\pi$
$104$	0.824720	+	2.26009i	0.0808705	+	0.221620i
$105$		0			0
$106$	0.340706	−	0.790444i	0.0330923	−	0.0767747i
$107$	1.23312			0.119210			0.0596052	−	0.998222i	$-0.481016\pi$
$107$	1.23312			0.119210			0.0596052	+	0.998222i	$0.481016\pi$
$108$	−9.77202	+	3.53662i	−0.940313	+	0.340312i
$109$	−3.20293			−0.306785			−0.153393	−	0.988165i	$-0.549020\pi$
$109$	−3.20293			−0.306785			−0.153393	+	0.988165i	$0.549020\pi$
$110$	7.34660	−	17.0442i	0.700471	−	1.62510i
$111$	−6.88114	+	2.80492i	−0.653128	+	0.266231i
$112$		0			0
$113$		−	19.9097i		−	1.87294i	−0.350744	−	0.936471i	$-0.614071\pi$
$113$		−	19.9097i		−	1.87294i	0.350744	−	0.936471i	$-0.385929\pi$
$114$	−0.175108	+	8.79533i	−0.0164003	+	0.823758i
$115$			15.7392i			1.46769i
$116$	−4.91346	+	4.64072i	−0.456203	+	0.430880i
$117$	1.82463	−	1.78394i	0.168687	−	0.164925i
$118$	10.2333	+	4.41088i	0.942052	+	0.406054i
$119$		0			0
$120$	14.4126	−	13.0797i	1.31568	−	1.19401i
$121$	−0.0872743			−0.00793402
$122$	12.6576	+	5.45582i	1.14596	+	0.493947i
$123$	−3.50140	−	8.58978i	−0.315711	−	0.774515i
$124$	7.12307	−	6.72769i	0.639671	−	0.604164i
$125$		−	22.9762i		−	2.05505i
$126$		0			0
$127$		−	16.4426i		−	1.45904i	−0.683957	−	0.729522i	$-0.739742\pi$
$127$		−	16.4426i		−	1.45904i	0.683957	−	0.729522i	$-0.260258\pi$
$128$	−10.8321	+	3.26569i	−0.957435	+	0.288649i
$129$	−5.01146	−	12.2943i	−0.441234	−	1.08245i
$130$	−1.89167	+	4.38871i	−0.165911	+	0.384915i
$131$	2.27690			0.198934			0.0994670	−	0.995041i	$-0.468286\pi$
$131$	2.27690			0.198934			0.0994670	+	0.995041i	$0.468286\pi$
$132$	10.4166	+	4.73791i	0.906646	+	0.412382i
$133$		0			0
$134$	−5.06366	+	11.7478i	−0.437434	+	1.01485i
$135$	−18.9357	−	8.22130i	−1.62973	−	0.707577i
$136$	1.53170	−	0.558928i	0.131343	−	0.0479277i
$137$		−	9.20432i		−	0.786378i	−0.919458	−	0.393189i	$-0.871372\pi$
$137$		−	9.20432i		−	0.786378i	0.919458	−	0.393189i	$-0.128628\pi$
$138$	−9.70224	−	0.193164i	−0.825910	−	0.0164432i
$139$			11.1056i			0.941960i	0.882144	+	0.470980i	$0.156100\pi$
$139$			11.1056i			0.941960i	−0.882144	+	0.470980i	$0.843900\pi$
$140$		0			0
$141$	14.5804	−	5.94333i	1.22789	−	0.500519i
$142$	11.8917	+	5.12568i	0.997927	+	0.430138i
$143$	−2.80991			−0.234976
$144$	7.88594	+	9.04500i	0.657162	+	0.753750i
$145$	−13.4253			−1.11491
$146$	1.83665	+	0.791654i	0.152002	+	0.0655177i
$147$		0			0
$148$	5.89167	+	6.23792i	0.484292	+	0.512754i
$149$		−	6.71741i		−	0.550311i	−0.961400	−	0.275156i	$-0.911271\pi$
$149$		−	6.71741i		−	0.550311i	0.961400	−	0.275156i	$-0.0887294\pi$
$150$	26.4085	+	0.525770i	2.15624	+	0.0429290i
$151$			13.2128i			1.07524i	0.843186	+	0.537622i	$0.180677\pi$
$151$			13.2128i			1.07524i	−0.843186	+	0.537622i	$0.819323\pi$
$152$	9.54251	−	3.48212i	0.773999	−	0.282437i
$153$	−1.20901	−	1.23658i	−0.0977425	−	0.0999718i
$154$		0			0
$155$	19.4628			1.56329
$156$	−2.68215	−	1.21996i	−0.214744	−	0.0976751i
$157$	2.38824			0.190602			0.0953011	−	0.995448i	$-0.469619\pi$
$157$	2.38824			0.190602			0.0953011	+	0.995448i	$0.469619\pi$
$158$	3.87830	−	8.99771i	0.308541	−	0.715820i
$159$	0.397925	+	0.976206i	0.0315575	+	0.0774182i
$160$	−20.0971	−	10.0585i	−1.58881	−	0.795196i
$161$		0			0
$162$	5.30032	−	11.5718i	0.416433	−	0.909167i
$163$			18.2918i			1.43272i	0.697728	+	0.716362i	$0.254194\pi$
$163$			18.2918i			1.43272i	−0.697728	+	0.716362i	$0.745806\pi$
$164$	−7.78685	+	7.35463i	−0.608051	+	0.574300i
$165$	8.58041	+	21.0498i	0.667984	+	1.63873i
$166$	5.37505	+	2.31681i	0.417185	+	0.179820i
$167$	19.3650			1.49851			0.749253	−	0.662284i	$-0.230413\pi$
$167$	19.3650			1.49851			0.749253	+	0.662284i	$0.230413\pi$
$168$		0			0
$169$	−12.2765			−0.944344
$170$	2.97431	+	1.28202i	0.228119	+	0.0983264i
$171$	−7.53211	−	7.70390i	−0.575994	−	0.589132i
$172$	−11.1451	+	10.5265i	−0.849806	+	0.802636i
$173$		−	5.58525i		−	0.424638i	−0.977200	−	0.212319i	$-0.931898\pi$
$173$		−	5.58525i		−	0.424638i	0.977200	−	0.212319i	$-0.0681016\pi$
$174$	0.164766	−	8.27589i	0.0124909	−	0.627394i
$175$		0			0
$176$	0.753784	−	13.1922i	0.0568186	−	0.994403i
$177$	−12.6382	+	5.15165i	−0.949948	+	0.387222i
$178$	−3.22254	+	7.47635i	−0.241540	+	0.560376i
$179$	−19.3794			−1.44848			−0.724241	−	0.689547i	$-0.757810\pi$
$179$	−19.3794			−1.44848			−0.724241	+	0.689547i	$0.757810\pi$
$180$	−0.948772	+	23.8181i	−0.0707173	+	1.77529i
$181$	−10.8735			−0.808222			−0.404111	−	0.914710i	$-0.632419\pi$
$181$	−10.8735			−0.808222			−0.404111	+	0.914710i	$0.632419\pi$
$182$		0			0
$183$	−15.6323	+	6.37208i	−1.15557	+	0.471038i
$184$	3.84117	+	10.5265i	0.283175	+	0.776021i
$185$			17.0442i			1.25312i
$186$	−0.238863	+	11.9976i	−0.0175143	+	0.879708i
$187$			1.90433i			0.139258i
$188$	−12.4838	−	13.2175i	−0.910477	−	0.963986i
$189$		0			0
$190$	18.5299	+	7.98697i	1.34430	+	0.579436i
$191$	1.23312			0.0892256			0.0446128	−	0.999004i	$-0.485795\pi$
$191$	1.23312			0.0892256			0.0446128	+	0.999004i	$0.485795\pi$
$192$	6.44711	−	12.2652i	0.465280	−	0.885163i
$193$	15.7833			1.13611			0.568055	−	0.822991i	$-0.307696\pi$
$193$	15.7833			1.13611			0.568055	+	0.822991i	$0.307696\pi$
$194$	17.5959	+	7.58437i	1.26331	+	0.544526i
$195$	−2.20936	−	5.42010i	−0.158216	−	0.388141i
$196$		0			0
$197$			17.3868i			1.23876i	0.785092	+	0.619379i	$0.212615\pi$
$197$			17.3868i			1.23876i	−0.785092	+	0.619379i	$0.787385\pi$
$198$	−13.0812	+	5.03096i	−0.929642	+	0.357535i
$199$			4.56759i			0.323788i	0.986808	+	0.161894i	$0.0517603\pi$
$199$			4.56759i			0.323788i	−0.986808	+	0.161894i	$0.948240\pi$
$200$	−10.4552	−	28.6519i	−0.739298	−	2.02600i
$201$	−5.91407	−	14.5086i	−0.417146	−	1.02336i
$202$	3.99654	−	9.27205i	0.281196	−	0.652379i
$203$		0			0
$204$	−0.826790	+	1.81775i	−0.0578869	+	0.127268i
$205$	−21.2765			−1.48601
$206$	−5.88266	+	13.6479i	−0.409865	+	0.950893i
$207$	8.49827	−	8.30877i	0.590671	−	0.577499i
$208$	−0.194091	+	3.39686i	−0.0134578	+	0.235530i
$209$			11.8639i			0.820646i
$210$		0			0
$211$			1.11224i			0.0765696i	0.999267	+	0.0382848i	$0.0121894\pi$
$211$			1.11224i			0.0765696i	−0.999267	+	0.0382848i	$0.987811\pi$
$212$	0.884955	−	0.835834i	0.0607790	−	0.0574053i
$213$	−14.6863	+	5.98651i	−1.00629	+	0.410189i
$214$	1.60147	+	0.690282i	0.109474	+	0.0471867i
$215$	−30.4524			−2.07684
$216$	−14.6707	−	0.877174i	−0.998217	−	0.0596841i
$217$		0			0
$218$	−4.15967	−	1.79295i	−0.281729	−	0.121434i
$219$	−2.26828	+	0.924607i	−0.153276	+	0.0624791i
$220$	19.0822	−	18.0230i	1.28652	−	1.21511i
$221$		−	0.490344i		−	0.0329841i
$222$	−10.5067	−	0.209180i	−0.705166	−	0.0140393i
$223$			23.6328i			1.58257i	0.611447	+	0.791285i	$0.290588\pi$
$223$			23.6328i			1.58257i	−0.611447	+	0.791285i	$0.709412\pi$
$224$		0			0
$225$	−23.1314	+	22.6156i	−1.54209	+	1.50770i
$226$	11.1451	−	25.8568i	0.741361	−	1.71997i
$227$	12.2983			0.816269			0.408135	−	0.912922i	$-0.366179\pi$
$227$	12.2983			0.816269			0.408135	+	0.912922i	$0.366179\pi$
$228$	−5.15089	+	11.3245i	−0.341126	+	0.749986i
$229$	−9.02948			−0.596685			−0.298342	−	0.954459i	$-0.596434\pi$
$229$	−9.02948			−0.596685			−0.298342	+	0.954459i	$0.596434\pi$
$230$	−8.81054	+	20.4406i	−0.580950	+	1.34781i
$231$		0			0
$232$	−8.97895	+	3.27647i	−0.589497	+	0.215111i
$233$		−	7.57382i		−	0.496178i	−0.968737	−	0.248089i	$-0.920197\pi$
$233$		−	7.57382i		−	0.496178i	0.968737	−	0.248089i	$-0.0798025\pi$
$234$	3.36828	−	1.29542i	0.220191	−	0.0846841i
$235$		−	36.1150i		−	2.35588i
$236$	10.8209	+	11.4569i	0.704383	+	0.745779i
$237$	4.52963	+	11.1123i	0.294231	+	0.721819i
$238$		0			0
$239$	−9.25206			−0.598466			−0.299233	−	0.954180i	$-0.596731\pi$
$239$	−9.25206			−0.598466			−0.299233	+	0.954180i	$0.596731\pi$
$240$	26.0395	−	8.91875i	1.68084	−	0.575703i
$241$	−15.6604			−1.00877			−0.504386	−	0.863478i	$-0.668281\pi$
$241$	−15.6604			−1.00877			−0.504386	+	0.863478i	$0.668281\pi$
$242$	−0.113344	−	0.0488547i	−0.00728601	−	0.00314050i
$243$	5.55718	+	14.5643i	0.356493	+	0.934298i
$244$	13.3844	+	14.1710i	0.856850	+	0.907207i
$245$		0			0
$246$	0.261122	−	13.1157i	0.0166485	−	0.836223i
$247$		−	3.05484i		−	0.194375i
$248$	13.0168	−	4.74992i	0.826570	−	0.301620i
$249$	−6.63824	+	2.70591i	−0.420681	+	0.171480i
$250$	12.8617	−	29.8394i	0.813446	−	1.88721i
$251$	3.08987			0.195031			0.0975155	−	0.995234i	$-0.468910\pi$
$251$	3.08987			0.195031			0.0975155	+	0.995234i	$0.468910\pi$
$252$		0			0
$253$	−13.0873			−0.822790
$254$	9.20430	−	21.3541i	0.577529	−	1.33988i
$255$	−3.67330	+	1.49733i	−0.230031	+	0.0937662i
$256$	−15.8959	−	1.82248i	−0.993492	−	0.113905i
$257$		−	7.36918i		−	0.459677i	−0.973229	−	0.229839i	$-0.926180\pi$
$257$		−	7.36918i		−	0.459677i	0.973229	−	0.229839i	$-0.0738198\pi$
$258$	0.373736	−	18.7721i	0.0232678	−	1.16870i
$259$		0			0
$260$	−4.91346	+	4.64072i	−0.304720	+	0.287805i
$261$	7.08727	+	7.24892i	0.438691	+	0.448697i
$262$	2.95703	+	1.27457i	0.182686	+	0.0787434i
$263$	22.2035			1.36913			0.684563	−	0.728954i	$-0.259993\pi$
$263$	22.2035			1.36913			0.684563	+	0.728954i	$0.259993\pi$
$264$	10.8759	+	11.9842i	0.669364	+	0.737576i
$265$	2.41801			0.148537
$266$		0			0
$267$	−3.76375	−	9.23337i	−0.230338	−	0.565073i
$268$	−13.1524	+	12.4224i	−0.803413	+	0.758817i
$269$		−	10.0139i		−	0.610556i	−0.952263	−	0.305278i	$-0.901251\pi$
$269$		−	10.0139i		−	0.610556i	0.952263	−	0.305278i	$-0.0987494\pi$
$270$	−19.9898	−	21.2770i	−1.21654	−	1.29487i
$271$		−	23.5847i		−	1.43267i	−0.697756	−	0.716335i	$-0.745818\pi$
$271$		−	23.5847i		−	1.43267i	0.697756	−	0.716335i	$-0.254182\pi$
$272$	2.30212	+	0.131539i	0.139586	+	0.00797574i
$273$		0			0
$274$	5.15243	−	11.9537i	0.311270	−	0.722151i
$275$	35.6221			2.14810
$276$	−12.4922	−	5.68202i	−0.751945	−	0.342018i
$277$	29.0598			1.74604			0.873018	−	0.487689i	$-0.162160\pi$
$277$	29.0598			1.74604			0.873018	+	0.487689i	$0.162160\pi$
$278$	−6.21671	+	14.4229i	−0.372853	+	0.865026i
$279$	−10.2745	−	10.5088i	−0.615117	−	0.629146i
$280$		0			0
$281$		−	23.2889i		−	1.38930i	−0.719347	−	0.694651i	$-0.755559\pi$
$281$		−	23.2889i		−	1.38930i	0.719347	−	0.694651i	$-0.244441\pi$
$282$	22.2627	+	0.443231i	1.32572	+	0.0263940i
$283$		−	17.4262i		−	1.03588i	−0.855416	−	0.517941i	$-0.826699\pi$
$283$		−	17.4262i		−	1.03588i	0.855416	−	0.517941i	$-0.173301\pi$
$284$	12.5745	+	13.3135i	0.746161	+	0.790013i
$285$	−22.8846	+	9.32833i	−1.35557	+	0.552562i
$286$	−3.64925	−	1.57294i	−0.215785	−	0.0930100i
$287$		0			0
$288$	5.17829	+	16.1612i	0.305134	+	0.952310i
$289$	16.6677			0.980452
$290$	−17.4356	−	7.51528i	−1.02385	−	0.441312i
$291$	−21.7311	+	8.85811i	−1.27390	+	0.519272i
$292$	1.94212	+	2.05625i	0.113654	+	0.120333i
$293$		−	1.20747i		−	0.0705412i	−0.999378	−	0.0352706i	$-0.988771\pi$
$293$		−	1.20747i		−	0.0705412i	0.999378	−	0.0352706i	$-0.0112293\pi$
$294$		0			0
$295$			31.3043i			1.82261i
$296$	4.15967	+	11.3993i	0.241776	+	0.662571i
$297$	6.83609	−	15.7452i	0.396670	−	0.913630i
$298$	3.76030	−	8.72395i	0.217828	−	0.505365i
$299$	3.36983			0.194882
$300$	34.0025	+	15.4658i	1.96314	+	0.892921i
$301$		0			0
$302$	−7.39632	+	17.1596i	−0.425610	+	0.987423i
$303$	4.66773	+	11.4511i	0.268154	+	0.657847i
$304$	14.3422	+	0.819488i	0.822579	+	0.0470009i
$305$			38.7203i			2.21712i
$306$	−0.877929	−	2.28274i	−0.0501878	−	0.130496i
$307$		−	34.0275i		−	1.94205i	−0.238973	−	0.971026i	$-0.576811\pi$
$307$		−	34.0275i		−	1.94205i	0.238973	−	0.971026i	$-0.423189\pi$
$308$		0			0
$309$	−6.87062	−	16.8553i	−0.390856	−	0.958863i
$310$	25.2765	+	10.8950i	1.43561	+	0.618792i
$311$	−26.7116			−1.51467			−0.757337	−	0.653024i	$-0.773500\pi$
$311$	−26.7116			−1.51467			−0.757337	+	0.653024i	$0.773500\pi$
$312$	−2.80042	−	3.08580i	−0.158543	−	0.174699i
$313$	−9.32552			−0.527110			−0.263555	−	0.964644i	$-0.584895\pi$
$313$	−9.32552			−0.527110			−0.263555	+	0.964644i	$0.584895\pi$
$314$	3.10162	+	1.33690i	0.175035	+	0.0754455i
$315$		0			0
$316$	10.0735	−	9.51439i	0.566681	−	0.535226i
$317$		−	26.9931i		−	1.51609i	−0.652205	−	0.758043i	$-0.726156\pi$
$317$		−	26.9931i		−	1.51609i	0.652205	−	0.758043i	$-0.273844\pi$
$318$	−0.0296758	+	1.49056i	−0.00166414	+	0.0835864i
$319$		−	11.1633i		−	0.625024i
$320$	−20.4697	−	24.3131i	−1.14429	−	1.35914i
$321$	−1.97783	+	0.806210i	−0.110392	+	0.0449982i
$322$		0			0
$323$	−2.07032			−0.115196
$324$	13.3613	−	12.0614i	0.742293	−	0.670075i
$325$	−9.17232			−0.508789
$326$	−10.2395	+	23.7557i	−0.567111	+	1.31571i
$327$	5.13724	−	2.09406i	0.284090	−	0.115802i
$328$	−14.2299	+	5.19256i	−0.785712	+	0.286711i
$329$		0			0
$330$	−0.639895	+	32.1407i	−0.0352251	+	1.76929i
$331$		−	14.5934i		−	0.802125i	−0.916051	−	0.401062i	$-0.868641\pi$
$331$		−	14.5934i		−	0.802125i	0.916051	−	0.401062i	$-0.131359\pi$
$332$	5.68370	+	6.01773i	0.311934	+	0.330266i
$333$	9.20293	−	8.99771i	0.504318	−	0.493072i
$334$	25.1494	+	10.8402i	1.37612	+	0.593149i
$335$	−35.9372			−1.96346
$336$		0			0
$337$	31.6823			1.72585			0.862924	−	0.505335i	$-0.168631\pi$
$337$	31.6823			1.72585			0.862924	+	0.505335i	$0.168631\pi$
$338$	−15.9436	−	6.87217i	−0.867215	−	0.373797i
$339$	13.0168	+	31.9334i	0.706978	+	1.73439i
$340$	3.14510	+	3.32994i	0.170567	+	0.180591i
$341$			16.1835i			0.876385i
$342$	−5.46949	−	14.2215i	−0.295756	−	0.769009i
$343$		0			0
$344$	−20.3668	+	7.43196i	−1.09810	+	0.400704i
$345$	−10.2902	−	25.2443i	−0.554006	−	1.35911i
$346$	3.12653	−	7.25360i	0.168083	−	0.389956i
$347$	2.15373			0.115618			0.0578092	−	0.998328i	$-0.481588\pi$
$347$	2.15373			0.115618			0.0578092	+	0.998328i	$0.481588\pi$
$348$	4.84669	−	10.6557i	0.259810	−	0.571207i
$349$	−33.0517			−1.76922			−0.884608	−	0.466335i	$-0.845574\pi$
$349$	−33.0517			−1.76922			−0.884608	+	0.466335i	$0.845574\pi$
$350$		0			0
$351$	−1.76022	+	4.05422i	−0.0939535	+	0.216398i
$352$	8.36375	−	16.7109i	0.445790	−	0.890695i
$353$		−	15.6070i		−	0.830678i	−0.909667	−	0.415339i	$-0.863663\pi$
$353$		−	15.6070i		−	0.830678i	0.909667	−	0.415339i	$-0.136337\pi$
$354$	−19.2972	−	0.384191i	−1.02563	−	0.0204195i
$355$			36.3773i			1.93071i
$356$	−8.37028	+	7.90567i	−0.443624	+	0.419000i
$357$		0			0
$358$	−25.1681	−	10.8483i	−1.33018	−	0.573348i
$359$	−33.6473			−1.77584			−0.887919	−	0.459999i	$-0.847850\pi$
$359$	−33.6473			−1.77584			−0.887919	+	0.459999i	$0.847850\pi$
$360$	−14.5651	+	30.4016i	−0.767650	+	1.60230i
$361$	6.10193			0.321154
$362$	−14.1215	−	6.08682i	−0.742211	−	0.319916i
$363$	0.139981	−	0.0570595i	0.00734708	−	0.00299485i
$364$		0			0
$365$			5.61842i			0.294082i
$366$	−23.8687	−	0.475206i	−1.24764	−	0.0248394i
$367$		−	7.84555i		−	0.409534i	−0.978811	−	0.204767i	$-0.934356\pi$
$367$		−	7.84555i		−	0.409534i	0.978811	−	0.204767i	$-0.0656437\pi$
$368$	−0.903988	+	15.8210i	−0.0471237	+	0.824728i
$369$	11.2319	+	11.4881i	0.584711	+	0.598047i
$370$	−9.54109	+	22.1355i	−0.496018	+	1.15077i
$371$		0			0
$372$	−7.02629	+	15.4477i	−0.364296	+	0.800926i
$373$	0.986273			0.0510673			0.0255336	−	0.999674i	$-0.491872\pi$
$373$	0.986273			0.0510673			0.0255336	+	0.999674i	$0.491872\pi$
$374$	−1.06601	+	2.47316i	−0.0551221	+	0.127884i
$375$	15.0217	+	36.8519i	0.775719	+	1.90303i
$376$	−8.81391	−	24.1539i	−0.454543	−	1.24564i
$377$			2.87443i			0.148040i
$378$		0			0
$379$		−	18.8285i		−	0.967153i	−0.875302	−	0.483576i	$-0.839337\pi$
$379$		−	18.8285i		−	0.967153i	0.875302	−	0.483576i	$-0.160663\pi$
$380$	19.5940	+	20.7455i	1.00515	+	1.06422i
$381$	10.7501	+	26.3726i	0.550744	+	1.35111i
$382$	1.60147	+	0.690282i	0.0819381	+	0.0353179i
$383$	−3.62288			−0.185120			−0.0925602	−	0.995707i	$-0.529505\pi$
$383$	−3.62288			−0.185120			−0.0925602	+	0.995707i	$0.529505\pi$
$384$	15.2388	−	12.3199i	0.777650	−	0.628697i
$385$		0			0
$386$	20.4979	+	8.83526i	1.04332	+	0.449703i
$387$	16.0759	+	16.4426i	0.817186	+	0.835824i
$388$	18.6063	+	19.6998i	0.944591	+	1.00010i
$389$		−	14.6161i		−	0.741067i	−0.928819	−	0.370534i	$-0.879175\pi$
$389$		−	14.6161i		−	0.741067i	0.928819	−	0.370534i	$-0.120825\pi$
$390$	0.164766	−	8.27589i	0.00834326	−	0.419066i
$391$		−	2.28380i		−	0.115497i
$392$		0			0
$393$	−3.65197	+	1.48863i	−0.184217	+	0.0750914i
$394$	−9.73284	+	22.5804i	−0.490333	+	1.13758i
$395$	27.5245			1.38491
$396$	−19.8049	−	0.788913i	−0.995236	−	0.0396443i
$397$	6.09704			0.306002			0.153001	−	0.988226i	$-0.451106\pi$
$397$	6.09704			0.306002			0.153001	+	0.988226i	$0.451106\pi$
$398$	−2.55687	+	5.93197i	−0.128164	+	0.297343i
$399$		0			0
$400$	2.46056	−	43.0631i	0.123028	−	2.15316i
$401$			7.29009i			0.364050i	0.983294	+	0.182025i	$0.0582651\pi$
$401$			7.29009i			0.364050i	−0.983294	+	0.182025i	$0.941735\pi$
$402$	0.441049	−	22.1531i	0.0219975	−	1.10489i
$403$		−	4.16708i		−	0.207577i
$404$	10.3807	−	9.80448i	0.516458	−	0.487791i
$405$	35.7463	+	0.806210i	1.77625	+	0.0400609i
$406$		0			0
$407$	−14.1724			−0.702502
$408$	−2.09130	+	1.89790i	−0.103535	+	0.0939599i
$409$	20.1900			0.998331			0.499165	−	0.866507i	$-0.333640\pi$
$409$	20.1900			0.998331			0.499165	+	0.866507i	$0.333640\pi$
$410$	−27.6319	−	11.9102i	−1.36464	−	0.588204i
$411$	6.01774	+	14.7630i	0.296833	+	0.728204i
$412$	−15.2797	+	14.4316i	−0.752778	+	0.710993i
$413$		0			0
$414$	15.6879	−	6.03347i	0.771018	−	0.296529i
$415$			16.4426i			0.807135i
$416$	−2.15358	+	4.30288i	−0.105588	+	0.210966i
$417$	−7.26076	−	17.8124i	−0.355561	−	0.872276i
$418$	−6.64124	+	15.4078i	−0.324834	+	0.753620i
$419$	1.32886			0.0649189			0.0324594	−	0.999473i	$-0.489666\pi$
$419$	1.32886			0.0649189			0.0324594	+	0.999473i	$0.489666\pi$
$420$		0			0
$421$	−7.31859			−0.356686			−0.178343	−	0.983968i	$-0.557074\pi$
$421$	−7.31859			−0.356686			−0.178343	+	0.983968i	$0.557074\pi$
$422$	−0.622613	+	1.44447i	−0.0303083	+	0.0703158i
$423$	−19.5001	+	19.0652i	−0.948125	+	0.926983i
$424$	1.61718	−	0.590120i	0.0785374	−	0.0286588i
$425$			6.21625i			0.301532i
$426$	−22.4244	−	0.446451i	−1.08647	−	0.0216306i
$427$		0			0
$428$	1.69343	+	1.79295i	0.0818549	+	0.0866655i
$429$	4.50686	−	1.83711i	0.217593	−	0.0886963i
$430$	−39.5488	−	17.0468i	−1.90721	−	0.822068i
$431$	−0.178929			−0.00861872			−0.00430936	−	0.999991i	$-0.501372\pi$
$431$	−0.178929			−0.00861872			−0.00430936	+	0.999991i	$0.501372\pi$
$432$	−18.5620	−	9.35163i	−0.893063	−	0.449931i
$433$	−15.2499			−0.732866			−0.366433	−	0.930444i	$-0.619421\pi$
$433$	−15.2499			−0.732866			−0.366433	+	0.930444i	$0.619421\pi$
$434$		0			0
$435$	21.5331	−	8.77742i	1.03243	−	0.420845i
$436$	−4.39853	−	4.65703i	−0.210652	−	0.223031i
$437$		−	14.2280i		−	0.680619i
$438$	−3.46342	−	0.0689537i	−0.165488	−	0.00329474i
$439$		−	29.9054i		−	1.42731i	−0.700499	−	0.713654i	$-0.747039\pi$
$439$		−	29.9054i		−	1.42731i	0.700499	−	0.713654i	$-0.252961\pi$
$440$	34.8711	−	12.7247i	1.66242	−	0.606626i
$441$		0			0
$442$	0.274487	−	0.636813i	0.0130560	−	0.0302901i
$443$	−5.01590			−0.238313			−0.119156	−	0.992876i	$-0.538019\pi$
$443$	−5.01590			−0.238313			−0.119156	+	0.992876i	$0.538019\pi$
$444$	−13.5281	−	6.15316i	−0.642014	−	0.292016i
$445$	−22.8706			−1.08417
$446$	−13.2293	+	30.6921i	−0.626424	+	1.45331i
$447$	4.39181	+	10.7742i	0.207725	+	0.509601i
$448$		0			0
$449$			14.4978i			0.684195i	0.939664	+	0.342098i	$0.111137\pi$
$449$			14.4978i			0.684195i	−0.939664	+	0.342098i	$0.888863\pi$
$450$	−42.7007	+	16.4224i	−2.01293	+	0.774161i
$451$		−	17.6916i		−	0.833064i
$452$	28.9485	−	27.3416i	1.36162	−	1.28604i
$453$	−8.63848	−	21.1923i	−0.405871	−	0.995700i
$454$	15.9719	+	6.88441i	0.749600	+	0.323101i
$455$		0			0
$456$	−13.0288	+	11.8239i	−0.610129	+	0.553704i
$457$	−19.8569			−0.928866			−0.464433	−	0.885608i	$-0.653742\pi$
$457$	−19.8569			−0.928866			−0.464433	+	0.885608i	$0.653742\pi$
$458$	−11.7267	−	5.05456i	−0.547951	−	0.236184i
$459$	2.74762	+	1.19293i	0.128248	+	0.0556813i
$460$	−22.8846	+	21.6144i	−1.06700	+	1.00777i
$461$			17.3910i			0.809978i	0.914322	+	0.404989i	$0.132725\pi$
$461$			17.3910i			0.809978i	−0.914322	+	0.404989i	$0.867275\pi$
$462$		0			0
$463$		−	15.3304i		−	0.712462i	−0.934398	−	0.356231i	$-0.884062\pi$
$463$		−	15.3304i		−	0.712462i	0.934398	−	0.356231i	$-0.115938\pi$
$464$	−13.4951	−	0.771091i	−0.626496	−	0.0357970i
$465$	−31.2167	+	12.7247i	−1.44764	+	0.590093i
$466$	4.23970	−	9.83619i	0.196401	−	0.455653i
$467$	21.0820			0.975557			0.487778	−	0.872968i	$-0.337807\pi$
$467$	21.0820			0.975557			0.487778	+	0.872968i	$0.337807\pi$
$468$	5.09956	+	0.203137i	0.235727	+	0.00938999i
$469$		0			0
$470$	20.2166	−	46.9028i	0.932521	−	2.16346i
$471$	−3.83054	+	1.56142i	−0.176502	+	0.0719464i
$472$	7.63986	+	20.9365i	0.351653	+	0.963682i
$473$		−	25.3215i		−	1.16428i
$474$	−0.337803	+	16.9672i	−0.0155158	+	0.779329i
$475$			38.7272i			1.77692i
$476$		0			0
$477$	−1.27648	−	1.30559i	−0.0584459	−	0.0597790i
$478$	−12.0157	−	5.17915i	−0.549586	−	0.236889i
$479$	7.59965			0.347237			0.173618	−	0.984813i	$-0.444454\pi$
$479$	7.59965			0.347237			0.173618	+	0.984813i	$0.444454\pi$
$480$	38.8103	+	2.99364i	1.77144	+	0.136641i
$481$	3.64925			0.166392
$482$	−20.3382	−	8.76642i	−0.926381	−	0.399299i
$483$		0			0
$484$	−0.119852	−	0.126896i	−0.00544784	−	0.00576800i
$485$			53.8268i			2.44415i
$486$	−0.935686	+	22.0255i	−0.0424436	+	0.999099i
$487$			15.4373i			0.699531i	0.936837	+	0.349765i	$0.113739\pi$
$487$			15.4373i			0.699531i	−0.936837	+	0.349765i	$0.886261\pi$
$488$	9.44975	+	25.8964i	0.427770	+	1.17228i
$489$	−11.9591	−	29.3386i	−0.540809	−	1.32674i
$490$		0			0
$491$	40.5166			1.82849			0.914243	−	0.405165i	$-0.132786\pi$
$491$	40.5166			1.82849			0.914243	+	0.405165i	$0.132786\pi$
$492$	7.68105	−	16.8872i	0.346288	−	0.761335i
$493$	1.94805			0.0877358
$494$	1.71005	−	3.96734i	0.0769387	−	0.178499i
$495$	−27.5245	−	28.1523i	−1.23714	−	1.26535i
$496$	19.5640	+	1.11786i	0.878450	+	0.0501932i
$497$		0			0
$498$	−10.1359	−	0.201796i	−0.454199	−	0.00904272i
$499$		−	30.3670i		−	1.35941i	−0.733484	−	0.679707i	$-0.762107\pi$
$499$		−	30.3670i		−	1.35941i	0.733484	−	0.679707i	$-0.237893\pi$
$500$	33.4072	−	31.5529i	1.49402	−	1.41109i
$501$	−31.0598	+	12.6607i	−1.38765	+	0.565640i
$502$	4.01284	+	1.72966i	0.179102	+	0.0771985i
$503$	13.8974			0.619652			0.309826	−	0.950793i	$-0.399729\pi$
$503$	13.8974			0.619652			0.309826	+	0.950793i	$0.399729\pi$
$504$		0			0
$505$	28.3638			1.26217
$506$	−16.9965	−	7.32604i	−0.755589	−	0.325682i
$507$	19.6905	−	8.02631i	0.874484	−	0.356461i
$508$	23.9074	−	22.5804i	1.06072	−	1.00184i
$509$		−	29.6562i		−	1.31449i	−0.753679	−	0.657243i	$-0.771722\pi$
$509$		−	29.6562i		−	1.31449i	0.753679	−	0.657243i	$-0.228278\pi$
$510$	−5.60872	−	0.111665i	−0.248358	−	0.00494461i
$511$		0			0
$512$	−19.6239	−	11.2651i	−0.867262	−	0.497853i
$513$	17.1176	+	7.43196i	0.755763	+	0.328129i
$514$	4.12515	−	9.57042i	0.181953	−	0.422133i
$515$	−41.7497			−1.83971
$516$	10.9937	−	24.1702i	0.483969	−	1.06403i
$517$	30.0299			1.32071
$518$		0			0
$519$	3.65161	+	8.95827i	0.160288	+	0.393225i
$520$	−8.97895	+	3.27647i	−0.393753	+	0.143683i
$521$			33.5702i			1.47074i	0.677667	+	0.735369i	$0.262991\pi$
$521$			33.5702i			1.47074i	−0.677667	+	0.735369i	$0.737009\pi$
$522$	5.14647	+	13.3816i	0.225255	+	0.585695i
$523$			10.1954i			0.445813i	0.974840	+	0.222906i	$0.0715544\pi$
$523$			10.1954i			0.445813i	−0.974840	+	0.222906i	$0.928446\pi$
$524$	3.12684	+	3.31060i	0.136596	+	0.144624i
$525$		0			0
$526$	28.8358	+	12.4291i	1.25730	+	0.541937i
$527$	−2.82410			−0.123020
$528$	7.41603	+	21.6521i	0.322741	+	0.942287i
$529$	−7.30486			−0.317603
$530$	3.14029	+	1.35357i	0.136406	+	0.0587951i
$531$	16.9026	−	16.5256i	0.733509	−	0.717152i
$532$		0			0
$533$			4.55539i			0.197316i
$534$	0.280686	−	14.0983i	0.0121465	−	0.610095i
$535$			4.89898i			0.211801i
$536$	−24.0350	+	8.77052i	−1.03815	+	0.378829i
$537$	31.0829	−	12.6702i	1.34133	−	0.546757i
$538$	5.60560	−	13.0051i	0.241675	−	0.560689i
$539$		0			0
$540$	−14.0504	−	38.8225i	−0.604633	−	1.67065i
$541$	10.3049			0.443041			0.221520	−	0.975156i	$-0.428898\pi$
$541$	10.3049			0.443041			0.221520	+	0.975156i	$0.428898\pi$
$542$	13.2023	−	30.6297i	0.567089	−	1.31566i
$543$	17.4402	−	7.10906i	0.748432	−	0.305079i
$544$	2.91614	+	1.45952i	0.125029	+	0.0625763i
$545$		−	12.7247i		−	0.545066i
$546$		0			0
$547$			5.44070i			0.232628i	0.993213	+	0.116314i	$0.0371078\pi$
$547$			5.44070i			0.232628i	−0.993213	+	0.116314i	$0.962892\pi$
$548$	13.3830	−	12.6401i	0.571694	−	0.539960i
$549$	20.9068	−	20.4406i	0.892281	−	0.872383i
$550$	46.2628	+	19.9407i	1.97265	+	0.850274i
$551$	12.1363			0.517025
$552$	−13.0431	−	14.3722i	−0.555150	−	0.611723i
$553$		0			0
$554$	37.7402	+	16.2672i	1.60343	+	0.691128i
$555$	−11.1434	−	27.3376i	−0.473013	−	1.16041i
$556$	−16.1474	+	15.2511i	−0.684801	+	0.646790i
$557$			4.43710i			0.188006i	0.995572	+	0.0940030i	$0.0299663\pi$
$557$			4.43710i			0.188006i	−0.995572	+	0.0940030i	$0.970034\pi$
$558$	−7.46088	−	19.3994i	−0.315844	−	0.821241i
$559$			6.52001i			0.275767i
$560$		0			0
$561$	−1.24504	−	3.05438i	−0.0525657	−	0.128956i
$562$	13.0368	−	30.2455i	0.549923	−	1.27583i
$563$	−39.1279			−1.64904			−0.824522	−	0.565830i	$-0.808556\pi$
$563$	−39.1279			−1.64904			−0.824522	+	0.565830i	$0.808556\pi$
$564$	28.6646	+	13.0379i	1.20700	+	0.548995i
$565$	79.0976			3.32766
$566$	9.75493	−	22.6316i	0.410030	−	0.951277i
$567$		0			0
$568$	8.87794	+	24.3294i	0.372510	+	1.02084i
$569$			44.4159i			1.86201i	0.365006	+	0.931005i	$0.381067\pi$
$569$			44.4159i			1.86201i	−0.365006	+	0.931005i	$0.618933\pi$
$570$	−34.9423	−	0.695672i	−1.46357	−	0.0291385i
$571$			2.49280i			0.104321i	0.998639	+	0.0521603i	$0.0166107\pi$
$571$			2.49280i			0.104321i	−0.998639	+	0.0521603i	$0.983389\pi$
$572$	−3.85880	−	4.08558i	−0.161345	−	0.170827i
$573$	−1.97783	+	0.806210i	−0.0826249	+	0.0336799i
$574$		0			0
$575$	−42.7205			−1.78157
$576$	−2.32171	+	23.8874i	−0.0967379	+	0.995310i
$577$	36.5866			1.52312			0.761560	−	0.648095i	$-0.224434\pi$
$577$	36.5866			1.52312			0.761560	+	0.648095i	$0.224434\pi$
$578$	21.6465	+	9.33030i	0.900374	+	0.388089i
$579$	−25.3152	+	10.3191i	−1.05206	+	0.428846i
$580$	−18.4368	−	19.5203i	−0.765546	−	0.810536i
$581$		0			0
$582$	−33.1809	−	0.660605i	−1.37539	−	0.0273830i
$583$			2.01060i			0.0832706i
$584$	1.37118	+	3.75764i	0.0567400	+	0.155492i
$585$	7.08727	+	7.24892i	0.293023	+	0.299706i
$586$	0.675922	−	1.56815i	0.0279221	−	0.0647797i
$587$	36.8412			1.52060			0.760299	−	0.649573i	$-0.225052\pi$
$587$	36.8412			1.52060			0.760299	+	0.649573i	$0.225052\pi$
$588$		0			0
$589$	−17.5941			−0.724954
$590$	−17.5236	+	40.6551i	−0.721437	+	1.67375i
$591$	−11.3674	−	27.8870i	−0.467592	−	1.14712i
$592$	−0.978945	+	17.1329i	−0.0402344	+	0.704157i
$593$			17.2194i			0.707118i	0.935412	+	0.353559i	$0.115029\pi$
$593$			17.2194i			0.707118i	−0.935412	+	0.353559i	$0.884971\pi$
$594$	17.6920	−	16.6217i	0.725911	−	0.681996i
$595$		0			0
$596$	9.76705	−	9.22491i	0.400074	−	0.377867i
$597$	−2.98627	−	7.32604i	−0.122220	−	0.299835i
$598$	4.37643	+	1.88638i	0.178965	+	0.0771397i
$599$	19.0215			0.777198			0.388599	−	0.921407i	$-0.372959\pi$
$599$	19.0215			0.777198			0.388599	+	0.921407i	$0.372959\pi$
$600$	35.5018	+	39.1197i	1.44936	+	1.59705i
$601$	7.95144			0.324346			0.162173	−	0.986762i	$-0.448150\pi$
$601$	7.95144			0.324346			0.162173	+	0.986762i	$0.448150\pi$
$602$		0			0
$603$	18.9713	+	19.4040i	0.772573	+	0.790194i
$604$	−19.2113	+	18.1450i	−0.781698	+	0.738308i
$605$		−	0.346725i		−	0.0140964i
$606$	−0.348102	+	17.4845i	−0.0141407	+	0.710260i
$607$		−	23.7840i		−	0.965364i	−0.875796	−	0.482682i	$-0.839663\pi$
$607$		−	23.7840i		−	0.965364i	0.875796	−	0.482682i	$-0.160337\pi$
$608$	18.1675	+	9.09279i	0.736791	+	0.368761i
$609$		0			0
$610$	−21.6750	+	50.2864i	−0.877596	+	2.03604i
$611$	−7.73239			−0.312819
$612$	0.137669	−	3.45607i	0.00556495	−	0.139703i
$613$	−29.7559			−1.20183			−0.600914	−	0.799313i	$-0.705197\pi$
$613$	−29.7559			−1.20183			−0.600914	+	0.799313i	$0.705197\pi$
$614$	19.0480	−	44.1918i	0.768717	−	1.78344i
$615$	34.1257	−	13.9105i	1.37608	−	0.560924i
$616$		0			0
$617$			28.7008i			1.15545i	0.816232	+	0.577724i	$0.196059\pi$
$617$			28.7008i			1.15545i	−0.816232	+	0.577724i	$0.803941\pi$
$618$	0.512385	−	25.7361i	0.0206111	−	1.03526i
$619$			22.9880i			0.923965i	0.886889	+	0.461983i	$0.152862\pi$
$619$			22.9880i			0.923965i	−0.886889	+	0.461983i	$0.847138\pi$
$620$	26.7279	+	28.2987i	1.07342	+	1.13650i
$621$	−8.19829	+	18.8827i	−0.328986	+	0.757737i
$622$	−34.6905	−	14.9527i	−1.39096	−	0.599549i
$623$		0			0
$624$	−1.90955	−	5.57518i	−0.0764431	−	0.223186i
$625$	37.3638			1.49455
$626$	−12.1111	−	5.22027i	−0.484058	−	0.208644i
$627$	−7.75659	−	19.0288i	−0.309768	−	0.759936i
$628$	3.27973	+	3.47248i	0.130875	+	0.138567i
$629$		−	2.47316i		−	0.0986115i
$630$		0			0
$631$		−	15.3304i		−	0.610292i	−0.952306	−	0.305146i	$-0.901295\pi$
$631$		−	15.3304i		−	0.610292i	0.952306	−	0.305146i	$-0.0987052\pi$
$632$	18.4086	−	6.71741i	0.732255	−	0.267204i
$633$	−0.727176	−	1.78394i	−0.0289027	−	0.0709052i
$634$	15.1103	−	35.0562i	0.600108	−	1.39226i
$635$	65.3236			2.59229
$636$	−0.872931	+	1.91919i	−0.0346140	+	0.0761008i
$637$		0			0
$638$	6.24902	−	14.4978i	0.247401	−	0.573975i
$639$	19.6417	−	19.2037i	0.777014	−	0.759688i
$640$	−12.9740	−	43.0342i	−0.512843	−	1.70108i
$641$			13.3989i			0.529223i	0.964355	+	0.264612i	$0.0852437\pi$
$641$			13.3989i			0.529223i	−0.964355	+	0.264612i	$0.914756\pi$
$642$	−3.01992	−	0.0601241i	−0.119187	−	0.00237291i
$643$		−	2.68122i		−	0.105737i	−0.998601	−	0.0528684i	$-0.983164\pi$
$643$		−	2.68122i		−	0.105737i	0.998601	−	0.0528684i	$-0.0168364\pi$
$644$		0			0
$645$	48.8432	−	19.9097i	1.92320	−	0.783942i
$646$	−2.68874	−	1.15893i	−0.105787	−	0.0455975i
$647$	19.7360			0.775902			0.387951	−	0.921680i	$-0.373183\pi$
$647$	19.7360			0.775902			0.387951	+	0.921680i	$0.373183\pi$
$648$	24.1041	−	8.18475i	0.946900	−	0.321527i
$649$	−26.0298			−1.02176
$650$	−11.9122	−	5.13452i	−0.467233	−	0.201392i
$651$		0			0
$652$	−26.5961	+	25.1198i	−1.04158	+	0.983769i
$653$		−	35.2227i		−	1.37837i	−0.724584	−	0.689186i	$-0.757968\pi$
$653$		−	35.2227i		−	1.37837i	0.724584	−	0.689186i	$-0.242032\pi$
$654$	7.84399	+	0.156167i	0.306724	+	0.00610663i
$655$			9.04574i			0.353446i
$656$	−21.3871	−	1.22203i	−0.835027	−	0.0477121i
$657$	3.03363	−	2.96599i	0.118353	−	0.115714i
$658$		0			0
$659$	−39.7628			−1.54894			−0.774469	−	0.632612i	$-0.781983\pi$
$659$	−39.7628			−1.54894			−0.774469	+	0.632612i	$0.781983\pi$
$660$	−18.8229	+	41.3832i	−0.732680	+	1.61084i
$661$	−14.9332			−0.580834			−0.290417	−	0.956900i	$-0.593794\pi$
$661$	−14.9332			−0.580834			−0.290417	+	0.956900i	$0.593794\pi$
$662$	8.16914	−	18.9525i	0.317503	−	0.736611i
$663$	0.320585	+	0.786471i	0.0124505	+	0.0305440i
$664$	4.01284	+	10.9969i	0.155728	+	0.426763i
$665$		0			0
$666$	16.9887	−	6.53375i	0.658298	−	0.253178i
$667$			13.3878i			0.518376i
$668$	26.5936	+	28.1565i	1.02894	+	1.08941i
$669$	−15.4510	−	37.9051i	−0.597371	−	1.46549i
$670$	−46.6719	−	20.1170i	−1.80309	−	0.777189i
$671$	−32.1963			−1.24292
$672$		0			0
$673$	1.52059			0.0586145			0.0293072	−	0.999570i	$-0.490670\pi$
$673$	1.52059			0.0586145			0.0293072	+	0.999570i	$0.490670\pi$
$674$	41.1461	+	17.7353i	1.58489	+	0.683137i
$675$	22.3149	−	51.3967i	0.858900	−	1.97826i
$676$	−16.8591	−	17.8499i	−0.648427	−	0.686534i
$677$			16.4053i			0.630508i	0.949007	+	0.315254i	$0.102090\pi$
$677$			16.4053i			0.630508i	−0.949007	+	0.315254i	$0.897910\pi$
$678$	−0.970748	+	48.7588i	−0.0372813	+	1.87257i
$679$		0			0
$680$	2.22052	+	6.08520i	0.0851532	+	0.233357i
$681$	−19.7255	+	8.04060i	−0.755883	+	0.308116i
$682$	−9.05926	+	21.0176i	−0.346897	+	0.804807i
$683$	−9.15654			−0.350365			−0.175183	−	0.984536i	$-0.556052\pi$
$683$	−9.15654			−0.350365			−0.175183	+	0.984536i	$0.556052\pi$
$684$	0.857679	−	21.5313i	0.0327942	−	0.823268i
$685$	36.5672			1.39716
$686$		0			0
$687$	14.4825	−	5.90343i	0.552543	−	0.225230i
$688$	−30.6108	−	1.74905i	−1.16703	−	0.0666820i
$689$		−	0.517708i		−	0.0197231i
$690$	0.767405	−	38.5453i	0.0292146	−	1.46740i
$691$		−	33.1654i		−	1.26167i	−0.775916	−	0.630836i	$-0.782712\pi$
$691$		−	33.1654i		−	1.26167i	0.775916	−	0.630836i	$-0.217288\pi$
$692$	8.12090	−	7.67013i	0.308710	−	0.291575i
$693$		0			0
$694$	2.79707	+	1.20562i	0.106175	+	0.0457649i
$695$	−44.1204			−1.67358
$696$	12.2593	−	11.1256i	0.464689	−	0.421714i
$697$	3.08727			0.116939
$698$	−42.9245	−	18.5018i	−1.62472	−	0.700304i
$699$	4.95173	+	12.1478i	0.187292	+	0.459472i
$700$		0			0
$701$		−	38.1529i		−	1.44101i	−0.693448	−	0.720507i	$-0.743909\pi$
$701$		−	38.1529i		−	1.44101i	0.693448	−	0.720507i	$-0.256091\pi$
$702$	−4.55550	+	4.27991i	−0.171936	+	0.161535i
$703$		−	15.4078i		−	0.581116i
$704$	20.2166	−	17.0207i	0.761941	−	0.641492i
$705$	23.6118	+	57.9254i	0.889272	+	2.18160i
$706$	8.73656	−	20.2690i	0.328805	−	0.762833i
$707$		0			0
$708$	−24.8464	−	11.3012i	−0.933783	−	0.424725i
$709$	13.9579			0.524200			0.262100	−	0.965041i	$-0.415585\pi$
$709$	13.9579			0.524200			0.262100	+	0.965041i	$0.415585\pi$
$710$	−20.3634	+	47.2435i	−0.764226	+	1.77302i
$711$	−14.5303	−	14.8617i	−0.544929	−	0.557358i
$712$	−15.2960	+	5.58161i	−0.573243	+	0.209180i
$713$		−	19.4083i		−	0.726848i
$714$		0			0
$715$		−	11.1633i		−	0.417483i
$716$	−26.6134	−	28.1774i	−0.994589	−	1.05304i
$717$	14.8395	−	6.04895i	0.554193	−	0.225902i
$718$	−43.6981	−	18.8352i	−1.63080	−	0.702925i
$719$	−20.1779			−0.752510			−0.376255	−	0.926516i	$-0.622788\pi$
$719$	−20.1779			−0.752510			−0.376255	+	0.926516i	$0.622788\pi$
$720$	−35.9342	+	31.3295i	−1.33919	+	1.16758i
$721$		0			0
$722$	7.92462	+	3.41576i	0.294924	+	0.127121i
$723$	25.1179	−	10.2387i	0.934146	−	0.380780i
$724$	−14.9324	−	15.8100i	−0.554959	−	0.587574i
$725$		−	36.4400i		−	1.35335i
$726$	0.213735	+	0.00425529i	0.00793245	+	0.000157929i
$727$		−	1.62103i		−	0.0601206i	−0.999548	−	0.0300603i	$-0.990430\pi$
$727$		−	1.62103i		−	0.0601206i	0.999548	−	0.0300603i	$-0.00956993\pi$
$728$		0			0
$729$	−18.4353	−	19.7266i	−0.682789	−	0.730615i
$730$	−3.14510	+	7.29669i	−0.116405	+	0.270063i
$731$	4.41873			0.163433
$732$	−30.7325	−	13.9785i	−1.13591	−	0.516659i
$733$	−27.8053			−1.02701			−0.513505	−	0.858086i	$-0.671653\pi$
$733$	−27.8053			−1.02701			−0.513505	+	0.858086i	$0.671653\pi$
$734$	4.39181	−	10.1891i	0.162105	−	0.376086i
$735$		0			0
$736$	−10.0304	+	20.0409i	−0.369725	+	0.738716i
$737$		−	29.8821i		−	1.10072i
$738$	8.15614	+	21.2071i	0.300232	+	0.780646i
$739$			28.9864i			1.06628i	0.846026	+	0.533142i	$0.178989\pi$
$739$			28.9864i			1.06628i	−0.846026	+	0.533142i	$0.821011\pi$
$740$	−24.7822	+	23.4066i	−0.911011	+	0.860443i
$741$	1.99724	+	4.89971i	0.0733704	+	0.179995i
$742$		0			0
$743$	10.4018			0.381604			0.190802	−	0.981629i	$-0.438891\pi$
$743$	10.4018			0.381604			0.190802	+	0.981629i	$0.438891\pi$
$744$	−17.7725	+	16.1288i	−0.651570	+	0.591312i
$745$	26.6871			0.977739
$746$	1.28088	+	0.552100i	0.0468964	+	0.0202138i
$747$	8.87808	−	8.68010i	0.324832	−	0.317588i
$748$	−2.76888	+	2.61518i	−0.101240	+	0.0956205i
$749$		0			0
$750$	−1.12027	+	56.2688i	−0.0409063	+	2.05465i
$751$		−	16.9792i		−	0.619581i	−0.950805	−	0.309791i	$-0.899741\pi$
$751$		−	16.9792i		−	0.619581i	0.950805	−	0.309791i	$-0.100259\pi$
$752$	2.07428	−	36.3028i	0.0756413	−	1.32383i
$753$	−4.95590	+	2.02014i	−0.180603	+	0.0736181i
$754$	−1.60906	+	3.73304i	−0.0585984	+	0.135949i
$755$	−52.4922			−1.91039
$756$		0			0
$757$	−10.9716			−0.398770			−0.199385	−	0.979921i	$-0.563894\pi$
$757$	−10.9716			−0.398770			−0.199385	+	0.979921i	$0.563894\pi$
$758$	10.5399	−	24.4527i	0.382825	−	0.888161i
$759$	20.9909	−	8.55640i	0.761922	−	0.310578i
$760$	13.8338	+	37.9107i	0.501806	+	1.37517i
$761$		−	11.6305i		−	0.421606i	−0.977529	−	0.210803i	$-0.932392\pi$
$761$		−	11.6305i		−	0.421606i	0.977529	−	0.210803i	$-0.0676078\pi$
$762$	−0.801702	+	40.2680i	−0.0290426	+	1.45876i
$763$		0			0
$764$	1.69343	+	1.79295i	0.0612660	+	0.0648666i
$765$	4.91273	−	4.80318i	0.177620	−	0.173659i
$766$	−4.70506	−	2.02803i	−0.170001	−	0.0732756i
$767$	6.70240			0.242010
$768$	26.6872	−	7.46954i	0.962991	−	0.269534i
$769$	−0.123424			−0.00445080			−0.00222540	−	0.999998i	$-0.500708\pi$
$769$	−0.123424			−0.00445080			−0.00222540	+	0.999998i	$0.500708\pi$
$770$		0			0
$771$	4.81794	+	11.8196i	0.173514	+	0.425671i
$772$	21.6750	+	22.9488i	0.780101	+	0.825947i
$773$			15.5446i			0.559100i	0.960131	+	0.279550i	$0.0901852\pi$
$773$			15.5446i			0.559100i	−0.960131	+	0.279550i	$0.909815\pi$
$774$	11.6736	+	30.3532i	0.419601	+	1.09102i
$775$			52.8274i			1.89762i
$776$	13.1365	+	35.9997i	0.471573	+	1.29231i
$777$		0			0
$778$	8.18188	−	18.9821i	0.293334	−	0.680541i
$779$	19.2337			0.689118
$780$	4.84669	−	10.6557i	0.173539	−	0.381536i
$781$	−30.2481			−1.08236
$782$	1.27843	−	2.96599i	0.0457167	−	0.106063i
$783$	−16.1067	−	6.99304i	−0.575607	−	0.249911i
$784$		0			0
$785$			9.48806i			0.338643i
$786$	−5.57615	−	0.111016i	−0.198895	−	0.00395983i
$787$			41.9211i			1.49433i	0.664640	+	0.747164i	$0.268585\pi$
$787$			41.9211i			1.49433i	−0.664640	+	0.747164i	$0.731415\pi$
$788$	−25.2802	+	23.8770i	−0.900571	+	0.850583i
$789$	−35.6126	+	14.5165i	−1.26784	+	0.516802i
$790$	35.7463	+	15.4078i	1.27180	+	0.548185i
$791$		0			0
$792$	−25.2792	−	12.1111i	−0.898258	−	0.430348i
$793$	8.29021			0.294394
$794$	7.91828	+	3.41303i	0.281009	+	0.121124i
$795$	−3.87830	+	1.58089i	−0.137549	+	0.0560683i
$796$	−6.64124	+	6.27260i	−0.235393	+	0.222327i
$797$			20.7831i			0.736175i	0.929791	+	0.368088i	$0.119987\pi$
$797$			20.7831i			0.736175i	−0.929791	+	0.368088i	$0.880013\pi$
$798$		0			0
$799$			5.24038i			0.185391i
$800$	27.3016	−	54.5490i	0.965257	−	1.92860i
$801$	12.0735	+	12.3488i	0.426595	+	0.436325i
$802$	−4.08088	+	9.46770i	−0.144101	+	0.334316i
$803$	−4.67177			−0.164863
$804$	12.9737	−	28.5235i	0.457548	−	1.00595i
$805$		0			0
$806$	2.33266	−	5.41181i	0.0821645	−	0.190623i
$807$	6.54702	+	16.0614i	0.230466	+	0.565389i
$808$	18.9699	−	6.92222i	0.667358	−	0.243523i
$809$			1.91423i			0.0673008i	0.999434	+	0.0336504i	$0.0107133\pi$
$809$			1.91423i			0.0673008i	−0.999434	+	0.0336504i	$0.989287\pi$
$810$	45.9727	+	21.0573i	1.61532	+	0.739876i
$811$		−	4.68171i		−	0.164397i	−0.996616	−	0.0821986i	$-0.973806\pi$
$811$		−	4.68171i		−	0.164397i	0.996616	−	0.0821986i	$-0.0261942\pi$
$812$		0			0
$813$	15.4196	+	37.8280i	0.540789	+	1.32668i
$814$	−18.4059	−	7.93350i	−0.645125	−	0.278069i
$815$	−72.6702			−2.54552
$816$	−3.77840	+	1.29414i	−0.132271	+	0.0453038i
$817$	27.5286			0.963105
$818$	26.2209	+	11.3020i	0.916792	+	0.395166i
$819$		0			0
$820$	−29.2186	−	30.9358i	−1.02036	−	1.08033i
$821$		−	1.67167i		−	0.0583416i	−0.999574	−	0.0291708i	$-0.990713\pi$
$821$		−	1.67167i		−	0.0583416i	0.999574	−	0.0291708i	$-0.00928667\pi$
$822$	−0.448781	+	22.5414i	−0.0156530	+	0.786222i
$823$			27.4309i			0.956182i	0.878310	+	0.478091i	$0.158671\pi$
$823$			27.4309i			0.956182i	−0.878310	+	0.478091i	$0.841329\pi$
$824$	−27.9225	+	10.1891i	−0.972725	+	0.354953i
$825$	−57.1350	+	23.2896i	−1.98918	+	0.810840i
$826$		0			0
$827$	−25.9621			−0.902789			−0.451395	−	0.892324i	$-0.649073\pi$
$827$	−25.9621			−0.902789			−0.451395	+	0.892324i	$0.649073\pi$
$828$	23.7514	+	0.946117i	0.825419	+	0.0328798i
$829$	−29.1349			−1.01190			−0.505948	−	0.862564i	$-0.668857\pi$
$829$	−29.1349			−1.01190			−0.505948	+	0.862564i	$0.668857\pi$
$830$	−9.20430	+	21.3541i	−0.319486	+	0.741213i
$831$	−46.6096	+	18.9992i	−1.61687	+	0.659074i
$832$	−5.20555	+	4.38265i	−0.180470	+	0.151941i
$833$		0			0
$834$	0.541480	−	27.1975i	0.0187499	−	0.941774i
$835$			76.9337i			2.66240i
$836$	−17.2501	+	16.2926i	−0.596606	+	0.563490i
$837$	23.3500	+	10.1379i	0.807095	+	0.350416i
$838$	1.72580	+	0.743872i	0.0596166	+	0.0256966i
$839$	−14.3863			−0.496671			−0.248336	−	0.968674i	$-0.579884\pi$
$839$	−14.3863			−0.496671			−0.248336	+	0.968674i	$0.579884\pi$
$840$		0			0
$841$	17.5804			0.606221
$842$	−9.50471	−	4.09683i	−0.327554	−	0.141186i
$843$	15.2262	+	37.3535i	0.524418	+	1.28652i
$844$	−1.61718	+	1.52742i	−0.0556658	+	0.0525759i
$845$		−	48.7723i		−	1.67782i
$846$	−35.9973	+	13.8443i	−1.23761	+	0.475978i
$847$		0			0
$848$	2.43059	+	0.138880i	0.0834668	+	0.00476916i
$849$	11.3932	+	27.9503i	0.391014	+	0.959250i
$850$	−3.47976	+	8.07309i	−0.119355	+	0.276905i
$851$	16.9965			0.582634
$852$	−28.8728	−	13.1326i	−0.989167	−	0.449917i
$853$	−49.4483			−1.69308			−0.846539	−	0.532327i	$-0.821318\pi$
$853$	−49.4483			−1.69308			−0.846539	+	0.532327i	$0.821318\pi$
$854$		0			0
$855$	30.6062	−	29.9237i	1.04671	−	1.02337i
$856$	1.19560	+	3.27647i	0.0408649	+	0.111987i
$857$			11.5797i			0.395554i	0.980247	+	0.197777i	$0.0633722\pi$
$857$			11.5797i			0.395554i	−0.980247	+	0.197777i	$0.936628\pi$
$858$	6.88148	+	0.137005i	0.234930	+	0.00467726i
$859$			7.24881i			0.247326i	0.992324	+	0.123663i	$0.0394642\pi$
$859$			7.24881i			0.247326i	−0.992324	+	0.123663i	$0.960536\pi$
$860$	−41.8198	−	44.2775i	−1.42604	−	1.50985i
$861$		0			0
$862$	−0.232377	−	0.100162i	−0.00791479	−	0.00341152i
$863$	20.8869			0.711000			0.355500	−	0.934676i	$-0.384311\pi$
$863$	20.8869			0.711000			0.355500	+	0.934676i	$0.384311\pi$
$864$	−18.8717	−	22.5357i	−0.642028	−	0.766681i
$865$	22.1892			0.754456
$866$	−19.8052	−	8.53667i	−0.673009	−	0.290088i
$867$	−26.7336	+	10.8973i	−0.907920	+	0.370090i
$868$		0			0
$869$			22.8869i			0.776385i
$870$	32.8787	+	0.654587i	1.11469	+	0.0221926i
$871$			7.69432i			0.260712i
$872$	−3.10548	−	8.51036i	−0.105165	−	0.288197i
$873$	29.0635	−	28.4154i	0.983649	−	0.961714i
$874$	7.96462	−	18.4781i	0.269407	−	0.625030i
$875$		0			0
$876$	−4.45937	−	2.02831i	−0.150668	−	0.0685304i
$877$	−57.1755			−1.93068			−0.965339	−	0.260998i	$-0.915948\pi$
$877$	−57.1755			−1.93068			−0.965339	+	0.260998i	$0.915948\pi$
$878$	16.7406	−	38.8384i	0.564967	−	1.31073i
$879$	0.789439	+	1.93668i	0.0266271	+	0.0653227i
$880$	52.4105	+	2.99465i	1.76676	+	0.100950i
$881$			26.8284i			0.903870i	0.892051	+	0.451935i	$0.149266\pi$
$881$			26.8284i			0.903870i	−0.892051	+	0.451935i	$0.850734\pi$
$882$		0			0
$883$			27.6059i			0.929012i	0.885570	+	0.464506i	$0.153768\pi$
$883$			27.6059i			0.929012i	−0.885570	+	0.464506i	$0.846232\pi$
$884$	0.712956	−	0.673381i	0.0239793	−	0.0226483i
$885$	−20.4666	−	50.2095i	−0.687978	−	1.68777i
$886$	−6.51419	−	2.80782i	−0.218849	−	0.0943306i
$887$	26.3406			0.884430			0.442215	−	0.896909i	$-0.354193\pi$
$887$	26.3406			0.884430			0.442215	+	0.896909i	$0.354193\pi$
$888$	−14.1246	−	15.5640i	−0.473990	−	0.522292i
$889$		0			0
$890$	−29.7022	−	12.8026i	−0.995622	−	0.429144i
$891$	−0.670371	+	29.7234i	−0.0224583	+	0.995772i
$892$	−34.3619	+	32.4546i	−1.15052	+	1.08666i
$893$			32.6475i			1.09251i
$894$	−0.327525	+	16.4510i	−0.0109541	+	0.550202i
$895$		−	76.9909i		−	2.57352i
$896$		0			0
$897$	−5.40493	+	2.20318i	−0.180465	+	0.0735621i
$898$	−8.11566	+	18.8285i	−0.270823	+	0.628314i
$899$	16.5551			0.552142
$900$	−64.6488	−	2.57523i	−2.15496	−	0.0858409i
$901$	−0.350860			−0.0116889
$902$	9.90347	−	22.9762i	0.329749	−	0.765024i
$903$		0			0
$904$	52.9010	−	19.3039i	1.75946	−	0.642038i
$905$		−	43.1986i		−	1.43597i
$906$	0.644226	−	32.3582i	0.0214030	−	1.07503i
$907$			10.9883i			0.364862i	0.983219	+	0.182431i	$0.0583966\pi$
$907$			10.9883i			0.364862i	−0.983219	+	0.182431i	$0.941603\pi$
$908$	16.8891	+	17.8817i	0.560485	+	0.593424i
$909$	−14.9733	−	15.3148i	−0.496634	−	0.507961i
$910$		0			0
$911$	6.42795			0.212968			0.106484	−	0.994314i	$-0.466041\pi$
$911$	6.42795			0.212968			0.106484	+	0.994314i	$0.466041\pi$
$912$	−23.5394	+	8.06245i	−0.779468	+	0.266974i
$913$	−13.6722			−0.452483
$914$	−25.7883	−	11.1156i	−0.853001	−	0.367670i
$915$	−25.3152	−	62.1042i	−0.836894	−	2.05310i
$916$	−12.4000	−	13.1288i	−0.409709	−	0.433787i
$917$		0			0
$918$	2.90057	+	3.08734i	0.0957331	+	0.101898i
$919$		−	55.1437i		−	1.81902i	−0.415677	−	0.909512i	$-0.636455\pi$
$919$		−	55.1437i		−	1.81902i	0.415677	−	0.909512i	$-0.363545\pi$
$920$	−41.8198	+	15.2603i	−1.37876	+	0.503117i
$921$	22.2470	+	54.5773i	0.733065	+	1.79838i
$922$	−9.73518	+	22.5858i	−0.320611	+	0.743823i
$923$	7.78856			0.256364
$924$		0			0
$925$	−46.2628			−1.52111
$926$	8.58169	−	19.9097i	0.282012	−	0.654272i
$927$	22.0398	+	22.5425i	0.723882	+	0.740392i
$928$	−17.0946	−	8.55578i	−0.561158	−	0.280857i
$929$		−	47.9582i		−	1.57346i	−0.617299	−	0.786728i	$-0.711773\pi$
$929$		−	47.9582i		−	1.57346i	0.617299	−	0.786728i	$-0.288227\pi$
$930$	−47.6645	−	0.948960i	−1.56298	−	0.0311176i
$931$		0			0
$932$	11.0123	−	10.4010i	0.360719	−	0.340697i
$933$	42.8432	−	17.4639i	1.40262	−	0.571743i
$934$	27.3793	+	11.8013i	0.895878	+	0.386152i
$935$	−7.56556			−0.247420
$936$	6.50913	+	3.11847i	0.212757	+	0.101930i
$937$	36.7501			1.20057			0.600287	−	0.799784i	$-0.295053\pi$
$937$	36.7501			1.20057			0.600287	+	0.799784i	$0.295053\pi$
$938$		0			0
$939$	14.9574	−	6.09698i	0.488115	−	0.198968i
$940$	52.5108	−	49.5961i	1.71271	−	1.61765i
$941$			39.6155i			1.29143i	0.763579	+	0.645714i	$0.223440\pi$
$941$			39.6155i			1.29143i	−0.763579	+	0.645714i	$0.776560\pi$
$942$	−5.84881	−	0.116445i	−0.190564	−	0.00379398i
$943$			21.2169i			0.690919i
$944$	−1.79798	+	31.4671i	−0.0585193	+	1.02417i
$945$		0			0
$946$	14.1745	−	32.8852i	0.460854	−	1.06919i
$947$	11.8519			0.385134			0.192567	−	0.981284i	$-0.438319\pi$
$947$	11.8519			0.385134			0.192567	+	0.981284i	$0.438319\pi$
$948$	−9.93667	+	21.8463i	−0.322728	+	0.709536i
$949$	1.20293			0.0390488
$950$	−21.6788	+	50.2953i	−0.703355	+	1.63179i
$951$	17.6480	+	43.2948i	0.572275	+	1.40393i
$952$		0			0
$953$			39.8193i			1.28987i	0.764236	+	0.644937i	$0.223116\pi$
$953$			39.8193i			1.28987i	−0.764236	+	0.644937i	$0.776884\pi$
$954$	−0.926923	−	2.41013i	−0.0300102	−	0.0780310i
$955$			4.89898i			0.158527i
$956$	−12.7057	−	13.4524i	−0.410932	−	0.435082i
$957$	7.29850	+	17.9050i	0.235927	+	0.578786i
$958$	9.86972	+	4.25416i	0.318876	+	0.137446i
$959$		0			0
$960$	48.7274	+	25.6132i	1.57267	+	0.826664i
$961$	7.00000			0.225806
$962$	4.73931	+	2.04279i	0.152802	+	0.0658623i
$963$	2.64517	−	2.58619i	0.0852395	−	0.0833388i
$964$	−21.5061	−	22.7700i	−0.692666	−	0.733373i
$965$			62.7045i			2.01853i
$966$		0			0
$967$		−	23.4388i		−	0.753741i	−0.926266	−	0.376871i	$-0.877000\pi$
$967$		−	23.4388i		−	0.753741i	0.926266	−	0.376871i	$-0.123000\pi$
$968$	−0.0846189	−	0.231892i	−0.00271975	−	0.00745330i
$969$	3.32062	−	1.35357i	0.106674	−	0.0434828i
$970$	−30.1314	+	69.9053i	−0.967460	+	2.24452i
$971$	11.1144			0.356677			0.178338	−	0.983969i	$-0.442928\pi$
$971$	11.1144			0.356677			0.178338	+	0.983969i	$0.442928\pi$
$972$	−13.5447	+	28.0810i	−0.434447	+	0.900697i
$973$		0			0
$974$	−8.64155	+	20.0485i	−0.276893	+	0.642396i
$975$	14.7116	−	5.99682i	0.471150	−	0.192052i
$976$	−2.22392	+	38.9217i	−0.0711861	+	1.24585i
$977$			11.0714i			0.354206i	0.984192	+	0.177103i	$0.0566725\pi$
$977$			11.0714i			0.354206i	−0.984192	+	0.177103i	$0.943327\pi$
$978$	0.891865	−	44.7967i	0.0285187	−	1.43244i
$979$		−	19.0171i		−	0.607790i
$980$		0			0
$981$	−6.87062	+	6.71741i	−0.219362	+	0.214470i
$982$	52.6192	+	22.6805i	1.67915	+	0.723764i
$983$	31.9433			1.01883			0.509416	−	0.860520i	$-0.329861\pi$
$983$	31.9433			1.01883			0.509416	+	0.860520i	$0.329861\pi$
$984$	19.4286	−	17.6318i	0.619362	−	0.562083i
$985$	−69.0747			−2.20090
$986$	2.52995	+	1.09049i	0.0805700	+	0.0347282i
$987$		0			0
$988$	4.44171	−	4.19516i	0.141310	−	0.133466i
$989$			30.3672i			0.965621i
$990$	−19.9871	−	51.9694i	−0.635233	−	1.65170i
$991$		−	20.7846i		−	0.660245i	−0.943938	−	0.330122i	$-0.892910\pi$
$991$		−	20.7846i		−	0.660245i	0.943938	−	0.330122i	$-0.107090\pi$
$992$	24.7822	+	12.4034i	0.786835	+	0.393808i
$993$	9.54109	+	23.4066i	0.302777	+	0.742785i
$994$		0			0
$995$	−18.1463			−0.575275
$996$	−13.0506	−	5.93596i	−0.413523	−	0.188088i
$997$	−41.5370			−1.31549			−0.657745	−	0.753241i	$-0.728489\pi$
$997$	−41.5370			−1.31549			−0.657745	+	0.753241i	$0.728489\pi$
$998$	16.9990	−	39.4379i	0.538093	−	1.24838i
$999$	−8.87808	+	20.4484i	−0.280890	+	0.646959i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.e.f.491.23	yes	24
3.2	odd	2	inner	588.2.e.f.491.2	yes	24
4.3	odd	2	inner	588.2.e.f.491.4	yes	24
7.2	even	3		588.2.n.h.263.6		24
7.3	odd	6		588.2.n.d.275.1		24
7.4	even	3		588.2.n.d.275.2		24
7.5	odd	6		588.2.n.h.263.5		24
7.6	odd	2	inner	588.2.e.f.491.24	yes	24
12.11	even	2	inner	588.2.e.f.491.21	yes	24
21.2	odd	6		588.2.n.h.263.7		24
21.5	even	6		588.2.n.h.263.8		24
21.11	odd	6		588.2.n.d.275.11		24
21.17	even	6		588.2.n.d.275.12		24
21.20	even	2	inner	588.2.e.f.491.1	✓	24
28.3	even	6		588.2.n.h.275.8		24
28.11	odd	6		588.2.n.h.275.7		24
28.19	even	6		588.2.n.d.263.12		24
28.23	odd	6		588.2.n.d.263.11		24
28.27	even	2	inner	588.2.e.f.491.3	yes	24
84.11	even	6		588.2.n.h.275.6		24
84.23	even	6		588.2.n.d.263.2		24
84.47	odd	6		588.2.n.d.263.1		24
84.59	odd	6		588.2.n.h.275.5		24
84.83	odd	2	inner	588.2.e.f.491.22	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.e.f.491.1	✓	24	21.20	even	2	inner
588.2.e.f.491.2	yes	24	3.2	odd	2	inner
588.2.e.f.491.3	yes	24	28.27	even	2	inner
588.2.e.f.491.4	yes	24	4.3	odd	2	inner
588.2.e.f.491.21	yes	24	12.11	even	2	inner
588.2.e.f.491.22	yes	24	84.83	odd	2	inner
588.2.e.f.491.23	yes	24	1.1	even	1	trivial
588.2.e.f.491.24	yes	24	7.6	odd	2	inner
588.2.n.d.263.1		24	84.47	odd	6
588.2.n.d.263.2		24	84.23	even	6
588.2.n.d.263.11		24	28.23	odd	6
588.2.n.d.263.12		24	28.19	even	6
588.2.n.d.275.1		24	7.3	odd	6
588.2.n.d.275.2		24	7.4	even	3
588.2.n.d.275.11		24	21.11	odd	6
588.2.n.d.275.12		24	21.17	even	6
588.2.n.h.263.5		24	7.5	odd	6
588.2.n.h.263.6		24	7.2	even	3
588.2.n.h.263.7		24	21.2	odd	6
588.2.n.h.263.8		24	21.5	even	6
588.2.n.h.275.5		24	84.59	odd	6
588.2.n.h.275.6		24	84.11	even	6
588.2.n.h.275.7		24	28.11	odd	6
588.2.n.h.275.8		24	28.3	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29871 + 0.559784i) q^{2} +(-1.60392 + 0.653796i) q^{3} +(1.37328 + 1.45399i) q^{4} +3.97283i q^{5} +(-2.44900 - 0.0487576i) q^{6} +(0.969574 + 2.65705i) q^{8} +(2.14510 - 2.09727i) q^{9} +(-2.22392 + 5.15954i) q^{10} -3.30344 q^{11} +(-3.15325 - 1.43424i) q^{12} +0.850601 q^{13} +(-2.59742 - 6.37208i) q^{15} +(-0.228181 + 3.99349i) q^{16} -0.576468i q^{17} +(3.95988 - 1.52295i) q^{18} -3.59139i q^{19} +(-5.77645 + 5.45582i) q^{20} +(-4.29021 - 1.84921i) q^{22} +3.96171 q^{23} +(-3.29229 - 3.62779i) q^{24} -10.7833 q^{25} +(1.10468 + 0.476153i) q^{26} +(-2.06938 + 4.76630i) q^{27} +3.37929i q^{29} +(0.193706 - 9.72947i) q^{30} -4.89898i q^{31} +(-2.53183 + 5.05864i) q^{32} +(5.29845 - 2.15978i) q^{33} +(0.322697 - 0.748663i) q^{34} +(5.99525 + 0.238815i) q^{36} +4.29021 q^{37} +(2.01040 - 4.66416i) q^{38} +(-1.36429 + 0.556119i) q^{39} +(-10.5560 + 3.85195i) q^{40} +5.35550i q^{41} +7.66518i q^{43} +(-4.53656 - 4.80318i) q^{44} +(8.33208 + 8.52212i) q^{45} +(5.14510 + 2.21770i) q^{46} -9.09050 q^{47} +(-2.24494 - 6.55441i) q^{48} +(-14.0044 - 6.03634i) q^{50} +(0.376892 + 0.924607i) q^{51} +(1.16812 + 1.23677i) q^{52} -0.608639i q^{53} +(-5.35562 + 5.03163i) q^{54} -13.1240i q^{55} +(2.34803 + 5.76029i) q^{57} +(-1.89167 + 4.38871i) q^{58} +7.87961 q^{59} +(5.69797 - 12.5273i) q^{60} +9.74629 q^{61} +(2.74237 - 6.36234i) q^{62} +(-6.11985 + 5.15242i) q^{64} +3.37929i q^{65} +(8.09014 + 0.161068i) q^{66} +9.04574i q^{67} +(0.838179 - 0.791654i) q^{68} +(-6.35425 + 2.59015i) q^{69} +9.15654 q^{71} +(7.65239 + 3.66619i) q^{72} +1.41421 q^{73} +(5.57172 + 2.40159i) q^{74} +(17.2956 - 7.05010i) q^{75} +(5.22185 - 4.93200i) q^{76} +(-2.08312 - 0.0414733i) q^{78} -6.92820i q^{79} +(-15.8654 - 0.906525i) q^{80} +(0.202931 - 8.99771i) q^{81} +(-2.99792 + 6.95523i) q^{82} +4.13877 q^{83} +2.29021 q^{85} +(-4.29084 + 9.95483i) q^{86} +(-2.20936 - 5.42010i) q^{87} +(-3.20293 - 8.77742i) q^{88} +5.75676i q^{89} +(6.05039 + 15.7319i) q^{90} +(5.44055 + 5.76029i) q^{92} +(3.20293 + 7.85756i) q^{93} +(-11.8059 - 5.08871i) q^{94} +14.2680 q^{95} +(0.753530 - 9.76894i) q^{96} +13.5487 q^{97} +(-7.08622 + 6.92820i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{16} - 12 q^{18} - 24 q^{25} - 48 q^{30} + 12 q^{36} + 72 q^{46} - 24 q^{57} + 72 q^{58} + 72 q^{60} - 48 q^{64} + 108 q^{72} - 24 q^{78} - 24 q^{81} - 48 q^{85} - 48 q^{88} + 48 q^{93}+O(q^{100}) \) 24 * q - 24 * q^16 - 12 * q^18 - 24 * q^25 - 48 * q^30 + 12 * q^36 + 72 * q^46 - 24 * q^57 + 72 * q^58 + 72 * q^60 - 48 * q^64 + 108 * q^72 - 24 * q^78 - 24 * q^81 - 48 * q^85 - 48 * q^88 + 48 * q^93

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